Angle between $\vec{a}$ and  $\vec{b}$ is $120{^{\circ}}$. If $|\vec{b}|=2|\vec{a}|$ and the vectors , $\vec{a}+x\vec{b}$ ,   $\vec{a}-\vec{b}$ are at right angle, then $x=$

1

The probability that a man who is x years old will die in a year is p. Then, amongst n persons $A_1,A_2,\ldots A_n…

Topic: NIMCET 2021

2

If α≠β and $\alpha^2=5\alpha-3,\beta^2=5\beta-3$, then the equation whose roots are $\frac{\alpha}{\beta}$&nb…

Topic: NIMCET 2021

3

The eccentric angle of the extremities of latus-rectum of the ellipse $\frac{{x}^2}{{a}^2}^{}+\frac{{y}^2}{{b}^2}^{}=1$…

Topic: NIMCET 2021

4

Suppose $A_1,A_2,\ldots,A_{30}$ are 30 sets each with five elements and $B_1,B_2,B_3,\ldots,B_n$ ar…

Topic: NIMCET 2021

5

If n is an integer between 0 to 21, then find a value of n for which the value of $n!(21-n)!$ is  minimum

Topic: NIMCET 2021

6

If A={1,2,3,4} and B={3,4,5}, then the number of elements in (A∪B)×(A∩B)×(AΔB)

Topic: NIMCET 2021

7

If a variable takes values 0, 1, 2,…, 50 with frequencies $1,\, {{50}}_{{{C}}_1},{{50}}_{{{C}}_2},\ldots..,{{50}}_…

Topic: NIMCET 2021

8

If the system of equations $3x-y+4z=3$ ,  $x+2y-3z=-2$ , $6x+5y+λz=-3 $   has atleast one solution, then $λ=$

Topic: NIMCET 2021

9

Let $\vec{a}=\hat{i}+\hat{j}$ and  $\vec{b}=2\hat{i}-\hat{k}$, the point of intersection of the lines $\vec{r}\times\ve…

Topic: NIMCET 2021

10

If the vectors $a\hat{i}+\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k},\hat{i}+\hat{j}+c\hat{k}$ , $(a,b,c\ne1)$ are coplana…

Topic: NIMCET 2021

1

If a number x is selected at random from natural numbers 1,2,…,100, then the probability for $x+\frac{100}{x}{\gt}…

Topic: NIMCET 2021

2

If X and Y are two sets, then X∩Y ' ∩ (X∪Y) ' is 

Topic: NIMCET 2021

3

$\int {e}^x(\sinh x+\cosh x)dx$

Topic: NIMCET 2021

4

If $\vec{e_1}=(1,1,1)$ and $\vec{e_2}=(1,1,-1)$ and $\vec{a}$ and $\vec{b}$  an…

Topic: NIMCET 2021

5

If P(1,2), Q(4,6), R(5,7) and S(a,b) are the vertices of a parallelogram PQRS, then 

Topic: NIMCET 2021

6

If $a\, \cos \theta+b\, \sin \, \theta=2$ and $a\, \sin \, \theta-b\, \cos \, \theta=3$ , then ${a}^{2^{}}+{b}^2=$

Topic: NIMCET 2021

7

If three thrown of three dice, the probability of throwing triplets not more than twice is 

Topic: NIMCET 2021

8

$\int {3}^{{3}^{{3}^x}}.{3}^{{3}^x}.{3}^xdx$ is equal to

Topic: NIMCET 2021

9

There are 50 questions in a paper. Find the number of ways in which a student can attempt one or more questions :

Topic: NIMCET 2021

10

Consider the following frequency distribution table. Class Interval 10-20 20-30 30-40 40-5050-…

Topic: NIMCET 2021